The isospectral Dirac operator on the 4-dimensional orthogonal quantum sphere

DOI10.1007/s00220-008-0420-xzbMath1148.58015arXivmath/0611100OpenAlexW3104627036MaRDI QIDQ934610

Giovanni Landi, Francesco D'Andrea, Ludwik Dąbrowski

Publication date: 30 July 2008

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0611100

zbMATH Keywords

quantum groupnoncommutative geometryDirac operatorspectral tripleFredholm moduleorthogonal quantum 4-spherespinorial representation

Mathematics Subject Classification ID

Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Noncommutative global analysis, noncommutative residues (58J42)

Related Items (8)

A Dolbeault-Dirac spectral triple for the \(B_2\)-irreducible quantum flag manifold ⋮ Quantum isometries of the finite noncommutative geometry of the standard model ⋮ Dirac operator on the quantum fuzzy four-sphere SqF4 ⋮ Dirac operators on quantum projective spaces ⋮ Anti-selfdual connections on the quantum projective plane: monopoles ⋮ THE NONCOMMUTATIVE GEOMETRY OF THE QUANTUM PROJECTIVE PLANE ⋮ THE 3D SPIN GEOMETRY OF THE QUANTUM TWO-SPHERE ⋮ Spectral action on \(\mathrm{SU}_q(2)\)

Cites Work

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• The spectral geometry of the equatorial Podleś sphere
• Fredholm modules for quantum Euclidean spheres
• Gravity coupled with matter and the foundation of non-commutative geometry
• The Dirac operator on \(\text{SU}_{q}(2)\)
• Quantum spheres
• Twisted \(\text{SU}(2)\) group. An example of a non-commutative differential calculus
• Equivariant spectral triples on the quantum SU(2) group
• The local index formula in noncommutative geometry
• On the eigenfunctions of the Dirac operator on spheres and real hyperbolic spaces
• Local index formula on the equatorial Podleś sphere
• The local index formula for \(\text{SU}_{q}(2)\)
• SO(5)q and contraction: Chevalley basis representations for q-generic and root of unity
• CYCLIC COHOMOLOGY, QUANTUM GROUP SYMMETRIES AND THE LOCAL INDEX FORMULA FOR SU q (2)

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